Ranked 287 places below the world No.46, De Minaur showed why he was rated one of the country's brightest prospects, outlasting the Frenchman 6-3 3-6 7-6 (7-1) on Tuesday at Homebush.
"I wasn't really going to push myself too hard for results these couple of weeks but, well, the results I have been getting, I couldn't be any happier," he said on Tuesday.
And while he went down to Mischa Zverev on his tour tournament debut, he wasted no time getting his first ATP win of his burgeoning career with an impressive showing in his home town.
"I told myself that I was going to have some opportunities in the match. I thought that I was getting on his serve quite often," De Minaur said.
"I just thought to myself that one of these games, he was going to have a cheap game, where he was going to have a couple of loose errors. I was glad I was able to take that opportunity."
Hewitt doubled as De Minaur's mentor and was courtside at Ken Rosewell Arena on day three.
"It helps me relax a bit and just makes sure I focus on the next point," said De Minaur, who has also received a wildcard into next week's Australian Open in Melbourne.
"That helps me just play the match point by point and not get too ahead of myself. It's great to have him out there every match, just supporting me, in my corner.
"He's just pretty much told me to believe I can beat these guys. That goes a long way. It's important to not get out there already beaten on court."
Zverev beat Nicolas Almagro in straight sets.